The Eye of the Azure (蒼の眼 Ao no Me) is a power of the Successor of the Azure.
The Power of the Eye (眼の力 Me no Chikara) allows one to recognize the location of the Amaterasu Unit within the Boundary. This power also allows one to observe things that cannot normally be perceived.
In BlazBlue: Chronophantasma, Noel Vermillion used this power to expose the true form of the Sealed Weapon: Izayoi, and also to find the Kushinada's Lynchpin which was sealed in a place beyond perception.
Due to comments dropped by Rachel Alucard, it is also possible that becoming the Eye would make that being an immortal similar to her.
According to Rachel, Noel was selected as the "Eye" specifically for breaking the endless loop, even chosen in the exact moment she broke it, which was in accordance with the Master Unit's wishes.